Some New Developments In Volatility Calculations

If you're working with daily data (without access to intraday data) and need to calculate volatility, then using close-to-close squared returns is by far not the best way to go. Trades and quants know that it is a very noisy metric, and come up with few work-arounds. In this post I will do a very quick review of some available options, as well as new developments. I am not planning a thorough review or comparison, rather just to offer my personal opinion, based on practical experience of what works better.

Quants tend to like either modelling some long-term average of daily squared returns (which introduced autocorrelation), or using GARCH to filter out smooth volatility process based on the data. GARCH model of daily returns, in my experience, also performed quite poorly, especially in forecasting future volatility.

Traders tend to use ATR - average true range - as a measure of price variability (quick tip: daily volatility ≈ ATR / stock price / 1.6). Another very similar estimate based on squared range, called Parkinson's volatility estimator.

Better volatility estimates have been devised: Garman-Klass and Rogers-Satchell volatility estimators are much better than others mentioned above. Yang-Zhang estimator has theoretically even higher accuracy, but works only for multi-day estimates. Magdon-Ismail and Atiya published another estimator but (according to their own research) it works only slightly better than R-S and G-K estimators, while being much more complicated from computational point. A quick note about the formulas to the right - similar to Y-Z estimator, G-K and R-S can also be adjusted to include overnight return,
see e.g. this.


Recently there were three interesting developments in estimators based on OHLC data.

Last year Bruno Dupire introduced what he called a Move-based estimator, a volatility estimate that reflect the cost of option hedging. I have to honestly admit, that after reviewing the presentation several times I still don't understand how the estimator is derived. If you can explain it to me, please email or comment below.

Jerzy Pawlowski created a skew-like and moment like estimators based on OHLC data, here slides 6 and 7, with R code available here.

Finally, not quite recent (2008) but also important is this correlation formula from Rogers and Zhou.

Triple Expiration

Next time, for the first time in SPX history, we will have 3 expirations in one week: on Monday Feb 29 month-end options will expire, newly listed Wednesday weeklys will expire on Wednesday Mar 2, and "regular" weeklys on Friday Mar 4. All of the options expire in the PM. And I have positions in all 3.

Speaking of Wednesday weeklys, the launch was a clear success. On the first day of trading - this past Tuesday, quotes width was somewhat sporadic, but the last few days I see that the width is pretty much like a regular weekly expiration, with volume and open interest also at quite respectable levels.

Old VIX vs New VIX - Simple Explanation

CBOE started disseminating VIX index in 1993. At that time the index was based on OEX (S&P100) options, that were most liquid index options at the time, and was calculated using weighted average of Black-Scholes implied volatility of ATM options. Ten years later CBOE changed the calculating, moving from OEX to more liquid SPX options, and also, most importantly, completely changing the calculation formula.

This formula for new VIX is not intuitive, and is quite complicated, but I will explain both old VIX formula and new VIX formula in simple geometric terms. Let's create a chart of options prices, calls and puts, vs their strikes. You will end up with a chart that looks something like this -

 

If options are relatively expensive the lines would be higher; if options are relatively cheaper the the lines would be lower. At one point, these lines will intersect, and the strike where they intersect will be very close to where the underlying index is trading. And the height of the point where these lines intersect is (approximately) proportional to the old VIX value. If volatility is high, then options are expensive, and the height of intersection point will be higher. If volatility is low, the height will be proportionally lower.

The math behind this is based on approximation for the price of ATM straddle ≈ 0.8  * index price * volatility * √ time to expiration  In our case, volatility ≈ height of the intersection point (0.4 * index price * √ time to expiration  )

New VIX is calculated in a very different way, but also has the place on the chart. Take the area under the call and put curves, that looks like a curved pyramid.



















The area under the curve is (approximately) proportional to the square of the new VIX! This is something that I covered in a previous post, so for the sake of not repeating myself I will just summarize:

old VIX is proportional to the height of the pyramid, new VIX is proportional to the square of the area of the pyramid. 

This connects two ideas, and also shows how new VIX uses information from all options, as opposed to the original VIX that uses only ATM options.

CBOE to List SPX Wednesday-Expiring Weeklys Options


CBOE announced yesterday that they will start listing SPX weekly options series with the same expiration time as VIX options. While it is not clear from the press-release, the circular clearly states that new options will be PM-settled, adding half-day of basis risk for traders. Overall I think this contract specification is somewhat surprising, but let's go over the history of VIX to understand CBOE's position.

Original VIX, as introduced by CBOE in 1993 was based on OEX (S&P100) options, most liquid index options at the time, and calculated by interpolating Back-Scholes implied volatililities of ATM options; OTM options did not figure in the calculation. VIX was already in use for 10 years, when in 2003 CBOE updated VIX methodology in two ways - first, moving from OEX to SPX, more liquid index options market, and changing the calculation to be in line with a formula for a variance swap - an OTC instrument that allowed for a pure (as in no delta, no rebalancing required) bet on variance.

While not exactly the same (VIX is a square root of var-swap, a non-linear transformation which makes static replication impossible) VIX futures and options became a class of its own. The original foundation of VIX vs basket of 30 day SPX options became less important as VIX complex became the dominant market leading the price discovery in volatility.

However that led to some inconvenience for traders - if you have two correlated markets like SPX and VIX, and you treat them as observable (as opposed to some model based latent quantity) you would want to naturally trade one against the other. However with Wednesday vs Friday expiration this adds significantly to residual risk. But current solution (Wednesday PM) begs a question - why PM? Trading VIX vs SPX Wedensday options still leaves half-day of difference?

I called CBOE (so you don't have to) asking for a comment. After being transferred from one person to another I received an answer that can be summarized as "we cannot comment on product design decisions" . Basically what it means is that CBOE decided to add another day for expirations, and designed the product to be similar to existing weeklys (PM). They were not meant to perfectly align with VIX complex, despite what it says in the press-release.

FWIW I think this is actually an unfortunate decision, and lost opportunity for CBOE.




Manager Spotlight: John Dolan, independent market maker in CME Case-Shiller Index futures and options

OnlyVIX: Thank you very much for agreeing to this interview. Let’s start at the beginning - how did you come to become a market-maker in such an exotic product? Your background is in bond/bond derivatives trading, and you worked at some big funds. Did you see a big opportunity for Shiller Index futures in general, or a niche for yourself?

John Dolan: I actually backed into this role as it fit a number of my interests.  During 2006, in my capacity of Chief Investment Officer of a $20 billion asset management company that focused on deep RMBS credit (Hyperion-Brookfield Asset Management) I certainly had paid attention to the roll-out of housing futures.  At the time, I thought this was a useful tool, as while MBS analysts had models that predicted prepayment projections with incredible precision most of what you heard about home prices was that there had never been a national decline in home prices, and much of "analysis" ended at that.  There had been good (appropriate) awareness that increases in home price drove mortgage refinancing - which was generally good for RMBS credit, but most of what you read at the time was that home prices might rise between 5 and 10%.  In theory, the Case Shiller futures would become a market for public expectations.

Unfortunately (for the CME contracts), portfolio managers’ attention and trading shifted to the OTC ABX credit-default swaps (a more lucrative business for Wall Street, that better hedged their positions) and interest in the Case Shiller futures became incredibly one-sided (i.e. mostly sellers).
I left the asset management business in 2007 and found my way to litigation consulting, and eventually expert witness work (which I continue to do today, along with teaching).  Many of the questions in 2007-2009 were of a Watergate-like mindset, "what did they know and when did they know it?"  I became interested in addressing that question as it related to the decline in home prices, and thought that the futures (which were forward looking) might have given an earlier signal than the commonly referenced housing indices (as most were moving averages issued with a lag).
So as a former trader, and huge fan of futures as a hedge (I've traded gas, FX, S&P, T-bonds, coffee and cattle in my PA)  I looked into the contracts and noticed that they were quoted with very large bid/ask spreads – almost 20 points in some cases, and in other there were no quotes at all. Also forward curves had no consistent message - closes indicated that forward prices would be higher or lower, or in some cases both, with different slopes for different regions.  Having seen just what had happened in the 2006-07 housing collapse I thought that the market (and distressed RMBS and Whole Loan buyers) might be well served by a more robust market for housing futures, so I started bidding and offering.

After a while I grew frustrated that there were so few responses (counters) so I called the CME to inquire.  They told me that all of the market makers had either re-prioritized their efforts, or had left their firms, and that in fact there was no real market maker.  I don't recall who asked first, but I figured that if I was taking the risk of making markets, that I might as well have the upside of being known for that.  That role continues to open doors to meetings that might otherwise be a challenge to arrange.

And that's how I came to be the market maker in 2010.

OV: So now you have been doing it for five years; how is it working out?

JD: At one point I became quite obsessed with making sure that there were prices on all 121 contracts (11 regions* 11 expirations).   I think that may have diffused some potential trading interest, so later (and through today) I decided to just be more responsive to, and offer better quotes on, inquiries, offer a tighter set of bids and offers for the first 5 expirations (while continuing to maintain a full set on the 10-city index).  Bid/ask spreads are at historical narrow levels.  I try to keep at least one CUS contract (10-city index) under one point (bid/ask).


In the last five years I encouraged the CME to switch from having the contracts open 21 hours/day to today's ~8 hours, and also worked with the CME to reintroduce electronic options (but only on 4 regions to focus interest.).  However, that effort only resulted in one sizeable trade (35 lots) in 2014.  (BTW- I am taking another run at that with focus on the LAX Nov' 17 contract.)

OV: I can imagine that risk management can be quite difficult - there is no forward arbitrage (like VIX index, and other non-store-able commodities). Also, for you as a market maker there are additional issues (correct me if I'm wrong) – trading is sparse, and city-indexes are not correlated with anything?

JD: Yes, I have often been > 50% of quotes and open interest for last few years, there is no cash (OTC) market, and as such, there is no one to hedge with.   Beyond that, I've analyzed that home price futures are not highly correlated with anything.  So, maybe a good portfolio tool, but a lousy product to hedge.

For now, I just try not to get offside by more than 30 contracts ($1.5mm position) and try to bias the markets I quote to be more likely to get back to even.

Net, I use the market making role to be the sounding board for parties looking for other sides to trade with, and, in the past, have come close to brokering 50+ lots.   Keeping quotes posted keeps me current on issues related to home prices, which helps in other parts of my consulting business.
Success to me would be having some Wall Street firm realize the potential, make very tight 10x10 markets, and find a use for the futures in other products (e.g. an ETF, capital relief, etc.)

OV: So if this is such a big market AND if people have very recent memories of taking big losses, why is there not more trading in these futures?

JB: While there is some element of chicken-and-egg (i.e. limited trading because people don't see others trading) I sense that there may be a few other good reasons:

In my experience in talking to potential traders, while hedgers are happy to hedge using an index, most longs seem to be less enthusiastic about buying an index.  Real estate longs feel that it’s all about “location, location, location” and as such, active management (e.g. asset picking) prevails.  While there have been periods where asset selection provided great opportunities (e.g. S&L crises, post the 2007 crash), I tend to think that the equivalent of passive management, i.e. buying the performance of an index via a futures contract should appeal to some potential longs at some points in time.

Case Shiller futures represent the price of the index at a point in time.  Unfortunately, some longs would like to buy the spot index, and carry it (to ride the price rise), but can’t replicate that via futures.  Unlike forward S&P500 contracts, which trade versus spot based on carry (and anticipated dividends) Case Shiller futures are not spot levels carried forward.   One-year forward futures prices were ~8% higher than spot in 2012 reflecting a belief that the turn had come and that the percent of assets sold at distressed levels would decline.

Home price futures have exhibited almost no correlation to the stock market over the last two years. For example, the S&P is up ~300 points and the CUSX16 (10-city contract for Nov ’16) is flat. Traders express frustration that the futures can’t be hedged.  Great, I say, because as a portfolio manager I want assets that have low R^2 to the stock market.

A final angle is that there’s an element that the futures are “too good” a hedging asset.  Someone looking to hedge against a price decline could sell Nov ’17 contracts and never have to roll the position.  While that might work well for a hedger, the futures broker won’t see much trading. Brokers seem to prefer day traders and tight, deep markets.

Finally, I think that options, rather than futures might be a better retail product.  I’m working on that.

OV: Thank you very much, John!

John Dolan's website is HomePriceFutures.com where he writes about home price derivatives.

Some Vol Funds News

FINalternatives reports that recent large trades in crude may be linked to liquidation of Blueshift Energy Fund. New-York based fund had a strong start, returning 15% in its first 7 months of trading in 2013, and 9% in 2014. According to most recent fund data, the fund was managing $170M but had a difficult year, losing 8% in March, and being down more than 9% this year.
FINalternatives article. Fiscal times article

Blackheath Volatility Arbitrage Strategy is also apparently closing out - the fund information was removed from website leaving other two funds. Funds performance has been rocky - it lost 4% in 2013, 5% in 2014, and is down 23% for 2015.

True Partner Capital is expanding, and planing to open US office in Chicago. Hong-Kong based volatility fund profited from the turbulent markets 2 months, up 15% on the year according to recent bloomberg article. The fund was recently a winner of AsiaHedge 2015 award in the market neutral and arbitrage fund category.

MLKJ Day

Few months ago I posed a quick note on date count as it relates to MLKJ day. Recently I received an email from Luigi Ballabio that correction has been accepted and will become part of Quantlib 1.7. Thanks to John Orford for the suggestion!

Weekly market report

Wall st delivered a mixed bag of news with VIX, VNKY, and VSTOXX and their underlying markets almost unchanged. VXD - volatility index based...